#! /usr/bin/env python
#
def grid_side ( m, n ):

#*****************************************************************************80
#
## GRID_SIDE finds the smallest M-D grid containing at least N points.
#
#  Discussion:
#
#    Each coordinate of the grid will have N_SIDE distinct values.
#    Thus the total number of points in the grid is N_SIDE**M.
#    This routine seeks the smallest N_SIDE such that N <= N_SIDE**M.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 August 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer M, the spatial dimension.
#
#    Input, integer N, the number of points to generate.
#
#    Output, integer N_SIDE, the length of one side of the smallest
#    grid in M dimensions that contains at least N points.
#
  if ( n <= 0 ):

    n_side = 0

  elif ( m <= 0 ):

    n_side = -1

  else:

    exponent = 1.0 / float ( m )

    n_side = int ( ( float ( n ) ) ** exponent )

    if ( ( n_side ** m ) < n ):
      n_side = n_side + 1

  return n_side

def grid_side_test ( ):

#*****************************************************************************80
#
## GRID_SIDE_TEST tests GRID_SIDE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 August 2016
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'GRID_SIDE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  GRID_SIDE returns the smallest N_SIDE, such that' )
  print ( '  N <= NSIDE^M' )

  print ( '' )
  print ( '  M      N  NSIDE  NSIDE^M' )

  for m in range ( 2, 5 ):
    print ( '' )
    for n in [ 10, 100, 1000, 10000 ]:
      n_side = grid_side ( m, n )
      print ( '  %1d  %5d  %5d  %5d' % ( m, n, n_side, n_side ** m ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'GRID_SIDE_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  grid_side_test ( )
  timestamp ( )